Title:
Jacobi photonic lattices and their SUSY partners

Abstract: We present a classical analog of quantum optical deformed oscillators in
arrays of waveguides. The normal modes of these one-dimensional photonic
crystals are given in terms of Jacobi polynomials. We show that it is possible
to attack the problem via factorization by exploiting the quantum optical
analogy. This allows us to provide an unbroken supersymmetric partner of the
proposed Jacobi lattices. Thanks to the underlying SU(1,1) group symmetry of
the lattices, we present the analytic propagators and impulse functions for
these one-dimensional photonic crystals.